scholarly journals Existence Results for a Coupled System of Nonlinear Singular Fractional Differential Equations with Impulse Effects

2013 ◽  
Vol 2013 ◽  
pp. 1-21
Author(s):  
Yuji Liu ◽  
Juan J. Nieto ◽  
Óscar Otero-Zarraquiños
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Coupled System ◽  
Existence Results ◽  
Fractional Differential System ◽  
Singular Fractional Differential Equations ◽  
Singular Fractional Differential System ◽  
Fractional Differential

A boundary value problem for the singular fractional differential system with impulse effects is presented. By applying Schauder's fixed point theorem in a suitably Banach space, we obtain the existence of at least one solution for this problem. Two examples are presented to illustrate the main theorem.

scholarly journals Hyers–Ulam stability of a coupled system of fractional differential equations of Hilfer–Hadamard type

2019 ◽  
Vol 52 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Manzoor Ahmad ◽  
Akbar Zada ◽  
Jehad Alzabut
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Coupled System ◽  
Ulam Stability ◽  
Fractional Differential System ◽  
Different Types ◽  
Fractional Differential

AbstractIn this paper, existence and uniqueness of solution for a coupled impulsive Hilfer–Hadamard type fractional differential system are obtained by using Kransnoselskii’s fixed point theorem. Different types of Hyers–Ulam stability are also discussed.We provide an example demonstrating consistency to the theoretical findings.

scholarly journals Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tian Wang ◽  
Guo Chen ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

scholarly journals Positive Solutions for a Coupled System of Nonlinear Semipositone Fractional Boundary Value Problems

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
S. Nageswara Rao ◽  
M. Zico Meetei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Coupled System ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

In this paper, we consider a four-point coupled boundary value problem for system of the nonlinear semipositone fractional differential equation D0+αu(t)+λf(t,u(t),v(t))=0,  0<t<1, D0+αv(t)+μg(t,u(t),v(t))=0,  0<t<1, u(0)=v(0)=0,  a1D0+βu(1)=b1D0+βv(ξ), a2D0+βv(1)=b2D0+βu(η),  η,ξ∈(0,1), where the coefficients ai,bi,i=1,2 are real positive constants, α∈(1,2],β∈(0,1],D0+α, D0+β are the standard Riemann-Liouville derivatives. Values of the parameters λ and μ are determined for which boundary value problem has positive solution by utilizing a fixed point theorem on cone.

Existence results for positive solutions to iterative systems of four-point fractional-order boundary value problems in a Banach space

2018 ◽  
Vol 13 (04) ◽  
pp. 2050070
Author(s):  
Kapula Rajendra Prasad ◽  
Boddu Muralee Bala Krushna ◽  
L. T. Wesen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Existence Results ◽  
Iterative System ◽  
Iterative Systems ◽  
Eigenvalue Intervals

We investigate the eigenvalue intervals of [Formula: see text] for which the iterative system of four-point fractional-order boundary value problem has at least one positive solution by utilizing Guo–Krasnosel’skii fixed point theorem under suitable conditions. The obtained results in the paper are illustrated with an example for their feasibility.

Impulsive fractional differential inclusions with flux boundary conditions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 953-961
Author(s):  
Hilmi Ergören
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Existence Results ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Flux Boundary Conditions ◽  
Fractional Differential

In this work we investigate some existence results for solutions of a boundary value problem for impulsive fractional differential inclusions supplemented with fractional flux boundary conditions by applying Bohnenblust-Karlin?s fixed point theorem for multivalued maps.

scholarly journals A Study of Nonlinear Boundary Value Problem

2021 ◽  
Author(s):  
Noureddine Bouteraa ◽  
Habib Djourdem
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Higher Order ◽  
Nonlinear Boundary Value Problem ◽  
Point Boundary ◽  
Error Estimations ◽  
Fractional Differential

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

Weak Solutions for Fractional Differential Equations via Henstock–Kurzweil–Pettis Integrals

2020 ◽  
Vol 21 (2) ◽  
pp. 135-145 ◽  
Author(s):  
Haide Gou ◽  
Yongxiang Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Weak Solutions ◽  
Measure Of Noncompactness ◽  
Pettis Integral ◽  
Existence Of Weak Solutions ◽  
Fractional Differential

AbstractIn this paper, we used Henstock–Kurzweil–Pettis integral instead of classical integrals. Using fixed point theorem and weak measure of noncompactness, we study the existence of weak solutions of boundary value problem for fractional integro-differential equations in Banach spaces. Our results generalize some known results. Finally, an example is given to demonstrate the feasibility of our conclusions.

scholarly journals Existence Results for a Fully Fourth-Order Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yongxiang Li ◽  
Qiuyan Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fourier Analysis ◽  
Growth Condition ◽  
Fourth Order ◽  
Boundary Value ◽  
Existence Of Solution ◽  
Existence Results ◽  
Analysis Method

We discuss the existence of solution for the fully fourth-order boundary value problemu(4)=f(t,u,u′,u′′,u′′′),0≤t≤1,u(0)=u(1)=u′′(0)=u′′(1)=0. A growth condition onfguaranteeing the existence of solution is presented. The discussion is based on the Fourier analysis method and Leray-Schauder fixed point theorem.

scholarly journals Uniqueness of Positive Solutions for a Perturbed Fractional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chen Yang ◽  
Jieming Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Point Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear perturbed fractional two-point boundary value problem:D0+αu(t)+f(t,u,u',…,u(n-2))+g(t)=0, 0<t<1, n-1<α≤n, n≥2,u(0)=u'(0)=⋯=u(n-2)(0)=u(n-2)(1)=0, whereD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem of generalized concave operators. An example is given to illustrate the main result.

scholarly journals Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jun-Rui Yue ◽  
Jian-Ping Sun ◽  
Shuqin Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

We consider the following boundary value problem of nonlinear fractional differential equation:(CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, whereα∈(2,3]is a real number, CD0+αdenotes the standard Caputo fractional derivative, andf:[0,1]×[0,+∞)→[0,+∞)is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.

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